OLYMPIC-REVENGE 2016 Problem 4

Let $\Omega$ and $\Gamma$ two circumferences such that $\Omega$ is in interior of $\Gamma$ . Let $P$ a point on $\Gamma$ . Define points $A$ and $B$ distinct of $P$ on $\Gamma$ such that $PA$ and $PB$ are tangentes to $\Omega$ . Prove that when $P$ varies on $\Gamma$ , the line $AB$ is tangent to a fixed circunference.